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Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Yes

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?


    2. Relevant equations



    3. The attempt at a solution

    I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0.

    Any help or hints on if I'm headed in the right direction would be very much appreciated!

    Thank you in advance.
     
  2. jcsd
  3. Apr 26, 2012 #2
    Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

    You are right, using the rules you've learned about infinity limits will get us ((1/n)/(1+(1/n^2))) and the limit of that as n approaches infinity is 0.
     
  4. Apr 27, 2012 #3

    SammyS

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    Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

    Multiply the numerator & denominator by 1/n .
     
  5. Apr 27, 2012 #4
    Re: Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit? I think Ye

    If you're talking about the SEQUENCE, then it converges. Use a useful little rule known as L'Hôpital.

    If you're talking about the SERIES, use the Ratio or Integral tests. It diverges.
     
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